Absolutely right! Make all necessary assumptions.

Tonio : here's how I thought it related to the geometric theorem. The point of intersection of the medians is the center of gravity of the three vertices, assuming they have equal mass. With this in mind, the theorem you stated is a specific case of the following more general theorem : the center of mass of $\displaystyle m+n$ points of equal (nonzero

) mass, $\displaystyle n$ of which are blue and $\displaystyle m$ red, lies $\displaystyle n/m$ of the way along the segment joining the centers of mass of the red points and of the blue points. But we can also view the points as events in a real probability space, with the expectation replacing the center of mass...

Deadstar : that's essentially it. The point is just to have fun and to see what kind of unexpected theorems people will pull out of their hats.